6. Consider a control system given by1,2+3 u,1 3133.with r(0) = (1,0,0). Find a control input u : [0, +o0)-+ R that minimizesI (1)||? + u?(t)dt.If you are using any computational tools, you may express any relevant values or matrices rounded tothree decimals.

Answered: 6. Consider a control system given by 1…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

See similar textbooks

Similar questions

Consider the following LP model. Minimize Z= 6 x, + 3 x, + 4 x, +x, 2 x, - x, +x, - 6x, = 60 x, +x, + 2 x, 0 Convert the above LP model into standard form.
Although we used gradient descent to find the minimizer of ƒ in part (a), we can also use calculus to solve the problem directly. Show that the minimizer of f is â = (A" A + 71)-'A"b, where I is the 4 × 4 identity matrix. What is the exact numerical value of âî for the problem in (a) and how does it compare to your result from gradient descent? What to submnit: your working out.
2 Given that 3x1 + 2x2 + X3 = 1 X1 – X2+3x3 = 5 2x1 + 5x2 – 2x3 = 0 apply the method of row transformation to obtain the value of x1, X2, X3.
To check the quality of two brands of lightbulbs, their life in burning hours was es timated as under for 100 bulbs of each brand. Life (in hrs) Brand 0-50 50-100 100-150 150-200 200-250 No. of bulbs 15 20 18 25 22 A Brand 8 60 25 В () Which brand gives higher life? (ii) Which brand is more dependable?
A manufacturer produces three products: Product A, Product B and Product C. Tobe able to produce each product he uses a combination of three distinct inputsnamely Input I, Input II and Input III the supply of which is currently at 730, 350and 350 units respectively. Each unit of Product A requires 6 units of Input I, 3units of Input II and 4 units of Input III to be produced. Similarly, each unit ofProduct B requires 8 units of Input 1 and 4 units of Input II while Product C uses 5units of Input I, 1 unit of Input II and 3 units of Input III.(i) Let a, b and c represent the number of units produced of Products A, B and Crespectively. The manufacturer must decide what quantity of each product toproduce so that his entire supply of inputs is utilized. Formulate his/herdecision in the form of a system of three linear equations in the variables a, band c. [3 marks](ii) Rewrite the above system of linear equations in the matrix form Ax = b. [2 marks](iii) Hence or otherwise, determine how…
7.(0) What is the Fisher linear discriminant method. (b) Given the 2-d data below for two classes: al-[(1,1), (1,2), (1,4), (2,1), (3,1), (3,3)], m2-[(2,2), (3,2), (3,4), (5,1), (5,4), (5.5)). Determine the optimal projection line in a single dimension.
7. A consumer’s utility function is given by U=2*x*y+3*x where x and y denote the number of items of two goods (good 1 and good 2) that are bought. Each item costs €1 for good 1 and €2 for good 2. The consumer’s budget per day is €95, which is x+2y=95. If we use the Lagrange multiplier method to maximize the level of utility per day subject to that constraint. Find the values of “x” and “y” which maximize the level of utility subject to that constraint.
8. (a) A firm has production function q(k,l) = k1/312/3¸ where k denotes the capital used andl denotes the labour employed. Suppose that each unit of capital costs v dollars and each unit of labour costs w dollars, so that the capital and labour costs are vk + wl. Use the Lagrange multiplier method to determine the values of k and l that minimise the cost of producing Q units of the firm's good. Find the corresponding minimised value, C, of this cost and the value, A*, of the Lagrange multiplier corresponding to the optimising values of k and l. Show that aC X* =
10. Suppose A is the n x n zero matrix (where all entries of A are zero), describe the solution set of A = b %3D
Let T : R2 → R² be the linear transformation which rotates vectors counter-clockwise about the origin by 7T/3 radians (60 degrees). (i) Find the standard matrix of the linear transformation T. (ii) Use your matrix to rotate the vector v = counterclockwise about the origin by 4 T/3 radians.
Q1// Solve the following assignment matrix which lead to reduced costs with the total cost calculation. (Using Hungarian Method) Machine Worker M1| M2 | Мз | М4 W1 6. 8 9 3 W2 10 7 8 13 W3 9 2 13 15 W4 10 4 7 8
Find the maximum value of the function z = 8x-2y with the restrictions as shown by the feasible region above

SEE MORE QUESTIONS

Recommended textbooks for you

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Advanced Engineering Mathematics

Advanced Math

ISBN:

9780470458365

Author:

Erwin Kreyszig

Publisher:

Wiley, John & Sons, Incorporated

Numerical Methods for Engineers

Advanced Math

ISBN:

9780073397924

Author:

Steven C. Chapra Dr., Raymond P. Canale

Publisher:

McGraw-Hill Education

Introductory Mathematics for Engineering Applicat…

Advanced Math

ISBN:

9781118141809

Author:

Nathan Klingbeil

Publisher:

WILEY

Mathematics For Machine Technology

Advanced Math

ISBN:

9781337798310

Author:

Peterson, John.

Publisher:

Cengage Learning,

Basic Technical Mathematics

Advanced Math

ISBN:

9780134437705

Author:

Washington

Publisher:

PEARSON

Topology

Advanced Math

ISBN:

9780134689517

Author:

Munkres, James R.

Publisher:

Pearson,

SEE MORE TEXTBOOKS

6. Consider a control system given by 1 2 2 2 1 3 3 () u, ra, with r(0) (1,0,0). Find a control input u : [0, +o0) R that minimizes If you are using any computational tools, you may express any relevant values or matrices rounded to three decimals.